Hostas are tough as nails, they can be moved almost anytime of the year (as long as the soil isn't frozen).
There is however an ideal time: early summer.
Hostas start with foliage growth (spring). After that, the rootsystem expands, to allow the plant to get enough food for the new foliage (summer).
The optimal time for transplanting is just before the major root growth starts. In this way the plant will develop its new root system in the new location: it will restart to grow immediately.

Rob is right, but if you keep as much as you can of the soil around the roots, they wil normally accept it all growing season.
If you want to split them- the early summer - after the first flush is the best time.

There's an entry on dividing hostas at the Hosta FAQ. Basically it agrees with what is said above; see the "another opinion" link to get Bob Solberg's ideas re: spring vs. late summer dividing. Now, moving you really can do about any time, if you give the guy some TLC after. The big advantage to spring moving is that you don't have to wrestle with all the leaves!